Chapter 1 NWP (EES 753) (Reference) (Based on Lin 2007; Kalnay 2003; Yu Lec
Chapter 1 NWP (EES 753) (reference) (Based on Lin 2007; Kalnay 2003; Yu Lec. Note) Chapter 1 Introduction and Historical Review 1.0 Introduction Basically, numerical weather prediction uses numerical methods to approximate a set of partially differential equations on discrete grid points in a finite area to predict the weather systems and processes in a finite area for a certain time in the future. In order to numerically integrate the partial differential equations, which govern the atmospheric motions and processes, with time, one needs to start the integration at certain time. In order to do so, the meteorological variables need to be prescribed at this initial time, which are called initial conditions. Mathematically, this corresponds to solve an initial-value problem. Due to practical limitations, such as computing power, numerical methods, etc., we are forced to make the numerical integration for predicting weather systems in a finite area. In order to do so, it is necessary to specify the meteorological variables at the boundaries, which include upper, lower, and lateral boundaries, of the domain of interest. Mathematically, this corresponds to solve a boundary- value problem. Thus, mathematically, numerical weather prediction is equivalent to solving an initial- and boundary- value problem. For example, to solve the following simple one-dimensional partial differential equation, u u U F(t, x) , (1.1) t x where u is the horizontal wind speed in x-direction, U the constant basic or mean wind speed, and F(t, x) is a forcing function, it is necessary to specify the , the variable to be predicted, at an initial time, say to .
[Show full text]